The on-line condition monitoring of turbomachinery blades is of utmost importance to ensure the long term health and availability of such machines and as such has been an area of study since the late 1960s. As a result a number of on-line blade vibration measurement techniques are available, each with its own associated advantages and shortcomings. In general, on-blade sensor measurement techniques suffer from sensor lifespan, whereas non-contact techniques usually have measurement bandwidth limitations. One non-contact measurement technique that yields improvements in the area of measurement bandwidth is laser Doppler vibrometry. This thesis presents results and findings from utilizing laser Doppler vibrometry in an Eulerian fashion (i.e. a fixed reference frame) to measure on-line blade vibrations in axial-flow turbomachinery. With this measurement approach, the laser beam is focussed at a fixed point in space and measurements are available for the periods during which each blade sweeps through the beam. The characteristics of the measurement technique are studied analytically with an Euler-Bernoulli cantilever beam and experimental verification is performed. An approach for the numerical simulation of the measurement technique is then presented. Associated with the presented measurement technique are the short periods during which each blade is exposed to the laser beam. This characteristic yields traditional frequency domain signal processing techniques unsuitable for providing useful blade health indicators. To obtain frequency domain information from such short signals, it is necessary to employ non-standard signal processing techniques such as non-harmonic Fourier analysis. Results from experimental testing on a single-blade test rotor at a single rotor speed are presented in the form of phase angle trends obtained with non-harmonic Fourier analysis. Considering the maximum of absolute unwrapped phase angle trends around various reference frequencies, good indicators of blade health deterioration were obtained. These indicators were verified numerically. To extend the application of this condition monitoring approach, measurements were repeated on a five-blade test rotor at four different rotor speeds. Various damage cases were considered as well as different ELDV measurement positions. Using statistical parameters of the abovementioned indicators as well as time domain parameters, it is shown that with this condition monitoring approach, blade damage can successfully be identified and quantified with the aid of artificial neural networks.